i 9 4 SCIENCE PROGRESS 



Russell and Burali-Forti is practically the same as that sug- 

 gested by Jourdain in 1904 in which individuals were stated not 

 to form a class (" manifold ") unless they could be arranged in 

 a segment of the series W of all ordinal numbers. However, 

 both Jourdain 's solution and this one are rendered superfluous 

 by Russell's theory just mentioned. 



A new edition of E. V. Huntington's work, first published 

 in 1905, on the Continuum and other Types of Serial Order has 

 just been published (Cambridge, Mass., 191 7). 



Of recent papers on the theory of point-aggregates we may 

 notice those by P. Mahlo {Jahresber. der Deutschen Mathe- 

 matiker-Vereinigung, 191 6, 25, 163-208) on parts of the con- 

 tinuum of the same power as it, F. Hausdorff (Math. Ann. 

 191 5-6, 77, 430-7) in which he proves that a Borel's aggregate 

 is either finite or enumerable or of the power of the continuum, 

 P. Alexandroff (Compt. Rend. 191 6, 162, 323-5) on the power 

 of measurable aggregates, W. Sierpinski (ibid. 629-32) on a 

 Cantorian curve which contains a one-one and continuous 

 image of any given curve, and the same author (ibid. 716-7) 

 on a general property relating to the measure of the parts into 

 which any point-aggregate whatever can be decomposed. 



J. H. Kline (Bull. Amer. Math. Soc. 191 7, 23, 290-2) proves 

 a theorem that if M is a domain and G lt G 2 , G 3 , ... is an enumer- 

 able set of nowhere dense closed sets of points, no one of which 

 disconnects any domain, then M — (G x + G 2 -J- G 3 + . . .) is 

 connected. This theorem, which contains as a special case 

 a theorem which F. Hausdorff published in 191 4, was proved by 

 R. L. Moore in 1916 (cf. Science Progress, 1916, 11, 270) on 

 the basis of a system of axioms proposed by him. 



E. Wiechert (Gottinger Nachrichten, 1916, 124-41) shows 

 that there are many ways of explaining the motion of the 

 perihelion of Mercury apart from the " most radical theory of 

 relativity," and that one way of doing so is particularly simple 

 and corresponds with modern physical views. E. Papperitz 

 (Jahresber. der Deutschen Mathematiker-Vereinigung, 191 6, 25, 

 84-95) tries to show that classical physics is quite able to explain 

 Michelson's experiment. Further, L. Silberstein read to the 

 Royal Astronomical Society on April 13, 191 7 (Nature, 191 7, 

 99> 1 59); a paper giving a deduction from the classical theory, 

 as opposed to Einstein's most recent " generalised theory of 

 relativity," of the motion of the perihelion of Mercury. 



